Scaling of the rupture dynamics of polymer chains pulled at one end at a constant rate

Interplay between Viscoelasticity and Force Rate Affects Sequential Unfolding in Polyproteins Pulled at Constant Velocity

Polyproteins are unique constructs, comprised of folded protein domains in tandem and polymeric linkers. These macromolecules perform under biological stresses by modulating their response through partial unfolding and extending. Although these unfolding events are considered independent, a history dependence of forced unfolding within polyproteins was reported. Here we measure the unfolding of single poly(I91) octamers, complemented with Brownian dynamics simulations, displaying increasing hierarchy in unfolding-foces, accompanied by a decrease in the effective stiffness. This counters the existing understanding that relates stiffness with variations in domain size and probe stiffness, which is expected to reduce the unfolding forces with every consecutive unfolding event. We utilize a simple mechanistic viscoelastic model to show that two effects are combined within a sequential forced unfolding process: the viscoelastic properties of the growing linker chain lead to a hierarchy of the unfolding events, and force-rate application governs the unfolding kinetics.

Force-Induced Unravelling of DNA Origami

The mechanical properties of DNA nanostructures are of widespread interest as applications that exploit their stability under constant or intermittent external forces become increasingly common. We explore the force response of DNA origami in comprehensive detail by combining AFM single molecule force spectroscopy experiments with simulations using oxDNA, a coarse-grained model of DNA at the nucleotide level, to study the unravelling of an iconic origami system: the Rothemund tile. We contrast the force-induced melting of the tile with simulations of an origami 10-helix bundle. Finally, we simulate a recently proposed origami biosensor, whose function takes advantage of origami behavior under tension. We observe characteristic stick-slip unfolding dynamics in our force-extension curves for both the Rothemund tile and the helix bundle and reasonable agreement with experimentally observed rupture forces for these systems. Our results highlight the effect of design on force response: we observe regular, modular unfolding for the Rothemund tile that contrasts with strain-softening of the 10-helix bundle which leads to catastropic failure under monotonically increasing force. Further, unravelling occurs straightforwardly from the scaffold ends inward for the Rothemund tile, while the helix bundle unfolds more nonlinearly. The detailed visualization of the yielding events provided by simulation allows preferred pathways through the complex unfolding free-energy landscape to be mapped, as a key factor in determining relative barrier heights is the extensional release per base pair broken. We shed light on two important questions: how stable DNA nanostructures are under external forces and what design principles can be applied to enhance stability.

Theory of rapid force spectroscopy

In dynamic force spectroscopy, single (bio-)molecular bonds are actively broken to assess their range and strength. At low loading rates, the experimentally measured statistical distributions of rupture forces can be analysed using Kramers’ theory of spontaneous unbinding. The essentially deterministic unbinding events induced by the extreme forces employed to speed up full-scale molecular simulations have been interpreted in mechanical terms, instead. Here we start from a rigorous probabilistic model of bond dynamics to develop a unified systematic theory that provides exact closed-form expressions for the rupture force distributions and mean unbinding forces, for slow and fast loading protocols. Comparing them with Brownian dynamics simulations, we find them to work well also at intermediate pulling forces. This renders them an ideal companion to Bayesian methods of data analysis, yielding an accurate tool for analysing and comparing force spectroscopy data from a wide range of experiments and simulations.

Dynamic force spectroscopy is widely applied to probe molecular interactions by forcible bond breaking, but it currently lacks an analytical theory that spans the divide between experiment and simulation. Here, such a unified framework is developed and shown to be accurate for slow and fast loading.

Molecular dynamics simulation of rupture in glassy polymer bridges within filler aggregates

We present a series of nonequilibrium molecular dynamics simulations, investigating the rupture mechanisms in glassy polymer films confined between two solid surfaces. Such systems provide a useful model for the strong nonlinear reinforcement of rubber by colloidal filler particles. Depending on the degree of confinement three qualitatively different rupture modes have been found, which originate from the interplay of internal (polymer-polymer) and external (polymer-wall) interactions. In very thin films we observe the formation and stretching of many single-chain bridges between the confining surfaces. Progressing to thicker samples we observe fewer bridges, consisting of bundled polymer chains, and eventually just one large bridge in thick specimens. The yield stress and the elongational modulus of the polymer films have been calculated from the stress-strain curves at various temperatures and confinements and their behavior has been analyzed in terms of polymer-polymer and polymer-surface interaction energies. The thinnest films (5 monomer diameters) are always glassy in our simulations, while the others display a glass transition temperature around 0.50-0.55 (in units ε(0)/k(B) of the Lennard-Jones interaction energy), depending on their thickness. This range of values, which has been determined using both the nonequilibrium tensile simulations and equilibrium diffusion data, agrees with the transition temperature previously found by shear simulations [Baljon and Robbins, Science 271, 482 (1996)].

Out-of-equilibrium characteristics of a forced translocating chain through a nanopore

Polymer translocation through a nanopore in a thin membrane is studied using a coarse-grained bead-spring model and Langevin dynamics simulation with a particular emphasis to explore out of equilibrium characteristics of the translocating chain. We analyze the out of equilibrium chain conformations both at the cis and the trans side separately either as a function of the time during the translocation process or as as function of the monomer index m inside the pore. A detailed picture of translocation emerges by monitoring the center of mass of the translocating chain, longitudinal and transverse components of the gyration radii and the end to end vector. We observe that polymer configurations at the cis side are distinctly different from those at the trans side. During the translocation and immediately afterwards, the chain is clearly out of equilibrium, as different parts of the chain are characterized by a series of effective Flory exponents. We further notice that immediately after the translocation the last set of beads that have just translocated take a relatively compact structure compared to the first set of beads that translocated earlier and the chain immediately after translocation is described by an effective Flory exponent 0.45+/-0.01. The analysis of these results is further strengthened by looking at the conformations of chain segments of equal length as they cross from the cis to the trans side, We discuss implications of these results to the theoretical estimates and numerical simulation studies of the translocation exponent reported by various groups.